Spring-driven jumping robots use an energised spring for propulsion, while the onboard motor only serves as a spring-charging source. A common mechanism in designing these robots is the rhomboidal linkage, which has been combined with linear springs (spring-linkage) to create a nonlinear spring, thereby increasing elastic energy storage and jump height for a given motor force. The effectiveness of this spring-linkage has been examined for individual designs, but a generalised design theory of this class of system remains absent. This paper presents an energetics analysis of the spring-linkage and provides insight into designing an ideal constant force spring, which stores the maximum energy for a given motor force. A quasi-static analysis shows that the force-displacement relationship of the spring-linkage changes with the orientation and type of the spring, but is independent of the linkage scale. Combining different types and orientations of springs within the linkage enables higher elastic energy storage than using single springs. Placing two translational springs at the diagonals of the rhomboidal linkage creates an ideal spring that could increase the jump height of prior robots by 50-160%.

翻译：弹簧驱动跳跃机器人利用充能弹簧实现推进，而机载电机仅作为弹簧充能来源。此类机器人设计中常见的机构是菱形连杆机构，该机构与线性弹簧（弹簧-连杆机构）结合可形成非线性弹簧，从而在给定电机力下增加弹性储能和跳跃高度。尽管已有研究针对特定设计验证了这种弹簧-连杆机构的有效性，但此类系统的通用设计理论仍属空白。本文提出一种弹簧-连杆机构的能量学分析方法，为设计理想恒力弹簧（可在给定电机力下存储最大能量）提供理论依据。准静态分析表明：弹簧-连杆机构的力-位移关系随弹簧方向与类型变化，但与连杆尺度无关；在连杆机构中组合不同弹簧类型与方向，其弹性储能效果优于单一弹簧。在菱形连杆对角线位置安装两个平移弹簧可形成理想弹簧，能使现有机器人的跳跃高度提升50%-160%。